A382999 a(n) = Sum_{d|n} phi(n/d) * (-2)^(d-1).

1, -1, 6, -8, 20, -30, 70, -136, 270, -500, 1034, -2088, 4108, -8134, 16440, -32912, 65552, -130878, 262162, -524800, 1048740, -2096138, 4194326, -8390976, 16777300, -33550348, 67109418, -134225840, 268435484, -536855640, 1073741854, -2147516704, 4294969404

Offset: 1

Author

Seiichi Manyama, Apr 12 2025

Keywords

• sign

Crossrefs

Column k=2 of A382995.

Cf. A000010, A034738, A074763.

Programs

PARI

a(n) = sumdiv(n, d, eulerphi(n/d)*(-2)^(d-1));

Formula

a(n) = Sum_{k=1..n} (-2)^(gcd(n,k) - 1).

G.f.: Sum_{k>=1} phi(k) * x^k / (1 + 2*x^k).